Adiabatic quantum state generation and statistical zero knowledge
- D. Aharonov, A. Ta-Shma
- Physics, Computer ScienceSymposium on the Theory of Computing
- 7 January 2003
The ASG approach to quantum algorithms provides intriguing links between quantum computation and many different areas: the analysis of spectral gaps and groundstates of Hamiltonians in physics, rapidly mixing Markov chains, statistical zero knowledge, and quantum random walks.
Quantum walks on graphs
- D. Aharonov, A. Ambainis, J. Kempe, U. Vazirani
- Mathematics, PhysicsSymposium on the Theory of Computing
- 18 December 2000
A lower bound on the possible speed up by quantum walks for general graphs is given, showing that quantum walks can be at most polynomially faster than their classical counterparts.
Fault-tolerant quantum computation with constant error
- D. Aharonov, M. Ben-Or
- Computer ScienceSymposium on the Theory of Computing
- 14 November 1996
This paper shows how to perform fault tolerant quantum computation when the error probability, q, is smaller than some constant threshold, q.. the cost is polylogarithmic in time and space, and no measurements are used during the quantum computation.
Adiabatic quantum computation is equivalent to standard quantum computation
- D. Aharonov, W. V. Dam, J. Kempe, Zeph Landau, S. Lloyd, O. Regev
- Physics, Computer Science45th Annual IEEE Symposium on Foundations of…
- 18 May 2004
The model of adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its exact computational power has been unknown, so this result implies that the adiABatic computation model and the standard quantum circuit model are polynomially equivalent.
Quantum circuits with mixed states
- D. Aharonov, A. Kitaev, N. Nisan
- Computer ScienceSymposium on the Theory of Computing
- 23 May 1998
A solution for the subroutine problem: the general function that a quantum circuit outputs is a probabilistic function, but using pure state language, such a function can not be used as a black box in other computations.
Fault-Tolerant Quantum Computation with Constant Error Rate
- D. Aharonov, M. Ben-Or
- Computer ScienceSIAM journal on computing (Print)
- 14 November 1996
This paper provides a self-contained and complete proof of universal fault-tolerant quantum computation in the presence of local noise, and shows that local noise is in principle not an obstacle for scalable quantum computation.
A Polynomial Quantum Algorithm for Approximating the Jones Polynomial
- D. Aharonov, V. Jones, Zeph Landau
- Computer ScienceSymposium on the Theory of Computing
- 9 November 2005
An explicit and simplePolynomial quantum algorithm to approximate the Jones polynomial of an n strands braid with m crossings at any primitive root of unity e2πi/k, where the running time of the algorithm is polynometric in m, n and k.
Interactive Proofs For Quantum Computations
- D. Aharonov, M. Ben-Or, Elad Eban
- Computer ScienceInternational Conference on Supercomputing
- 30 October 2008
Any language in BQP has a QPIP, and moreover, a fault tolerant one, and two proofs are provided: the simpler one uses a new (possibly of independent interest) quantum authentication scheme (QAS) based on random Clifford elements, which is not fault tolerant.
The Power of Quantum Systems on a Line
- D. Aharonov, D. Gottesman, S. Irani, J. Kempe
- PhysicsIEEE Annual Symposium on Foundations of Computer…
- 28 May 2007
The proof of the QMA-completeness result requires an additional idea beyond the usual techniques in the area: Some illegal configurations cannot be ruled out by local checks, and are instead ruled out because they would, in the future, evolve into a state which can be seen locally to be illegal.
A Simple Proof that Toffoli and Hadamard are Quantum Universal
- D. Aharonov
- Physics, Philosophy
- 9 January 2003
Recently Shi proved that Toffoli and Hadamard are universal for quantum computation. This is perhaps the simplest universal set of gates that one can hope for, conceptually; It shows that one only…
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